Juncker, the president of the European Commission, said late Monday after talks with British Prime Minister Theresa May that lawmakers in the U.K.'s parliament now "have a fundamental choice to make" by approving or rejecting the withdrawal agreement.
The House of Commons overwhelmingly rejected the original agreement in January. May has been seeking changes from the EU that might persuade enough lawmakers to back the deal. Another vote is scheduled for Tuesday.
Juncker said "the agreement today is the best possible" and warned "there will be no new negotiations. It is this."
The British government says it has secured "legally binding changes" from the European Union to overcome a key stumbling block on the Brexit deal.
Cabinet office Minister David Lidington told the House of Commons on Monday night that the two sides agreed on a "joint instrument" clarifying the withdrawal deal.
The measure is intended to reassure Britain it won't be trapped forever in a mechanism designed to prevent a hard border between Ireland and Northern Ireland.
Concerns over the border measure were the main reason Britain's Parliament rejected the deal in January. Lawmakers are due to vote on it again Tuesday.
The changes fall short of demands of hardcore U.K. Brexiteers, but may persuade some lawmakers to switch their votes.
British Prime Minister Theresa May has arrived in France for Brexit late talks with EU chief Jean-Claude Juncker on the eve before the British Parliament votes again on a divorce agreement.
Juncker kissed May twice on the cheeks when she arrived at the European Parliament. EU Brexit negotiator Michel Barnier kissed her hand before they went inside.
Following technical talks over the weekend, both sides were expected to go over the phrasing in the part of the agreement dealing with the post-Brexit border on the island of Ireland.
The future border between EU member Ireland and Northern Ireland, a part of the U.K., was a sticking point during more than 18 months of negotiations. It also has prevented the deal May reached with the EU from being approved by British lawmakers.
A news conference is set for later Monday.
Irish Prime Minister Leo Varadkar has delayed a trip to the United States for an emergency government meeting on Brexit.
Varadkar had been set to leave Monday for a U.S. visit to coincide with St. Patrick's Day. But he decided to wait so his Cabinet could discuss possible progress in the Brexit process, as British Prime Minister Theresa May holds talks with top European Union officials.
Britain's Parliament is due to vote Tuesday on whether to approve May's Brexit divorce deal with the EU, which it already rejected once.
The main sticking point is a measure to ensure the border between Northern Ireland and Ireland remains open, a key issue for Varadkar's government.
May flew to Strasbourg, France, late Monday to try to secure a last-minute deal with the bloc.
The European Union's top legislative Brexit official holds out hope for progress in last-ditch efforts to provide an orderly Brexit since "catastrophe" would follow the U.K.'s departure from the bloc without a withdrawal agreement.
Guy Verhofstadt said he would be meeting with British Prime Minister Theresa May late Monday and hopes May's meeting with EU Commission President Jean-Claude Juncker proves productive "as a no-deal Brexit would be a catastrophe."
The talks are still centered on finding a compromise on post-Brexit travel and trade rules at the border between EU member Ireland and Northern Ireland, which is part of the U.K.
Any deal between May's government and EU leaders must be approved by the European Parliament, the EU's elected legislature.
The leader of the European Parliament says a disorderly Brexit most be avoided at all costs and plants to meet with British Prime Minister Theresa May to press home the point.
European Parliament President Antonio Tajani said Monday night as May was traveling to Strasbourg, France for talks with European Commission President Jean-Claude Juncker: "We must avoid the departure of the U.K. without agreement. That would harm all European citizens."
May is making a last-ditch attempt to get concessions from EU counterparts on elements of the agreement they all reached late last year.
Britain's House of Commons, which resoundingly rejected the deal once before, has another vote scheduled Tuesday.
In Strasbourg, where the EU's parliament is located, May is also slated to meet with the legislature's chief Brexit official, Guy Verhofstadt.
Prime Minister Theresa May is heading to France for face-to-face talks with EU leaders as she scrambles to save her Brexit deal from defeat in Parliament.
May's Downing St. office said she was flying Monday afternoon to Strasbourg, France, to meet European Commission President Jean-Claude Juncker.
May has been seeking changes from the EU to her divorce deal since lawmakers in Parliament resoundingly defeated it in January. But the bloc is unwilling to reopen the withdrawal agreement.
If May can secure a legally binding change on provisions for the Irish border, some lawmakers who opposed to deal may be persuaded to vote for it in the House of Commons on Tuesday.
Britain is due to leave the bloc in 18 days, on March 29.
German Chancellor Angela Merkel says that the European Union's executive Commission has made an "important offer" to Britain to unblock an impasse over the U.K.'s withdrawal agreement.
British lawmakers' opposition to the deal centers on concerns over arrangements for the Irish border. Prime Minister Theresa May's government has been seeking changes, but the EU refuses to reopen the agreement after long negotiations.
Merkel said in Berlin Monday it was "very welcome" that Commission president Jean-Claude Juncker and chief EU negotiator Michel Barnier made "a multitude of suggestions" over the weekend on how to define the so-called "backstop" meant to keep open the border between EU member Ireland and the U.K.'s Northern Ireland.
She added: "I think that an important offer has again been made to Britain, and now it is of course for Britain to respond to these offers."
Ireland's deputy prime minister says U.K. leader Theresa May is set to hold last-minute talks with European Union leaders to try to save her foundering Brexit divorce deal.
Simon Coveney says May will fly to Strasbourg, France, a seat of the European Parliament, on Monday "to try to finalize an agreement, if that's possible."
May's 10 Downing St. office would not confirm the trip.
Britain's Parliament is due to vote Tuesday on the withdrawal agreement, which it has already rejected once.
May's office says talks are continuing to try to secure changes to the deal that can win over opponents in Parliament. May has spoken by phone to European Commission President Jean-Claude Juncker twice in the past 24 hours.
British Prime Minister Theresa May still hopes to secure changes from the EU that can win U.K. lawmakers' backing for her Brexit deal, despite a lack of progress in last-minute talks.
European Commission spokesman Margaritis Schinas said Monday that "no further meetings at political level are scheduled."
But May's spokesman, James Slack, said "talks are ongoing" at a technical level, and there is "a shared determination by both sides to find a solution."
British lawmakers are scheduled to vote Tuesday on whether to approve May's Brexit deal, which they resoundingly rejected in January. They look set to defeat it a second time, with the U.K. due to leave the bloc on March 29.
Pro-Brexit lawmakers have urged May to postpone Tuesday's vote rather than risk another crushing defeat.
But Slack said the vote "will take place tomorrow."
British Prime Minister Theresa May is fighting to save her European Union divorce deal with the negotiations deadlocked a day before Parliament is scheduled to vote on the plan.
May promised lawmakers two weeks ago they would get a second vote on the deal by March 12, but hard-line Brexit supporters are warning she should postpone the vote rather than risk another crushing defeat.
The House of Commons overwhelmingly rejected the deal in January, primarily because of concerns over arrangements for the Irish border. "Technical" talks aimed at securing concessions from the EU failed to secure a breakthrough over the weekend.
Former chief whip Andrew Mitchell told the Times of London that "anything that avoids what looks like a massive defeat on Tuesday is worth considering."